The information that passes through radio channels is more often received with errors.
From the telecommunications point of view, this problem is resolved with the application of a correcting code which makes it possible to correct the errors.
What the correcting code will consider to be errors may result:    from physical transmission errors,    from modifications made intentionally by a hacker in order to spoof the receiver.
The conventional maximum security solution consists in forging an imprint of the message transmitted and in transmitting this imprint together with the message. On reception, an imprint of the received message is computed by the receiver and compared with the received imprint. If a single bit of these two imprints differs then the message is rejected because it is potentially modified by a hacker. In practice, the error-correction telecom layer has already been applied and has corrected the transmission errors.
This security solution may for some applications be maximalist. This is because some applications may not be corrupted significantly by a (fixed) minimum number of modified bits and this may not have any impact on the security of the system.
The problem is therefore how to guarantee the security while, if appropriate, allowing certain applications to be able to be corrupted by errors.
Thus, depending on the applications, the security policy of the system will be strict and will not tolerate any error or, on the other hand, will allow a predefined number of errors.
One approach known from the prior art consists in dividing the message authentication codes (MACs) into a plurality of blocks, but this does not solve the problem. This method makes it possible to reject messages of smaller size and, in addition, the size of the MACs being smaller, the probability of errors is lower.
The article by Ch. G. Boncelet, entitled “The NTMAC for authentication of noisy messages” IEEE Transactions on Information Forensics and Security Vol. 1 No. 1, March 2006 is an illustration of this type of approach.
Despite all the advantages offered by implementing the systems of the prior art, the latter do however present the following drawbacks:    the prior solutions do not allow for the correction of the transmitted errors,    the error correction layer is applied upstream for “TELECOM” purposes,    the prior solutions try to approach a solution by reducing the size of the MACs, without however solving the problem posed.